(x-xy)dy+(y+xy)dx=0

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Solution for (x-xy)dy+(y+xy)dx=0 equation:


Simplifying
(x + -1xy) * dy + (y + xy) * dx = 0

Reorder the terms for easier multiplication:
dy(x + -1xy) + (y + xy) * dx = 0
(x * dy + -1xy * dy) + (y + xy) * dx = 0
(dxy + -1dxy2) + (y + xy) * dx = 0

Reorder the terms:
dxy + -1dxy2 + (xy + y) * dx = 0

Reorder the terms for easier multiplication:
dxy + -1dxy2 + dx(xy + y) = 0
dxy + -1dxy2 + (xy * dx + y * dx) = 0

Reorder the terms:
dxy + -1dxy2 + (dxy + dx2y) = 0
dxy + -1dxy2 + (dxy + dx2y) = 0

Reorder the terms:
dxy + dxy + -1dxy2 + dx2y = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + -1dxy2 + dx2y = 0

Solving
2dxy + -1dxy2 + dx2y = 0

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), 'dxy'.
dxy(2 + -1y + x) = 0

Subproblem 1

Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(2 + -1y + x)' equal to zero and attempt to solve: Simplifying 2 + -1y + x = 0 Reorder the terms: 2 + x + -1y = 0 Solving 2 + x + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + x + -2 + -1y = 0 + -2 Reorder the terms: 2 + -2 + x + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x + -1y = 0 + -2 x + -1y = 0 + -2 Combine like terms: 0 + -2 = -2 x + -1y = -2 Add '-1x' to each side of the equation. x + -1x + -1y = -2 + -1x Combine like terms: x + -1x = 0 0 + -1y = -2 + -1x -1y = -2 + -1x Add 'y' to each side of the equation. -1y + y = -2 + -1x + y Combine like terms: -1y + y = 0 0 = -2 + -1x + y Simplifying 0 = -2 + -1x + y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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